Problem: Simplify the following expression: $t = \dfrac{y^2 - 11y + 30}{y - 5} $
Solution: First factor the polynomial in the numerator. $ y^2 - 11y + 30 = (y - 5)(y - 6) $ So we can rewrite the expression as: $t = \dfrac{(y - 5)(y - 6)}{y - 5} $ We can divide the numerator and denominator by $(y - 5)$ on condition that $y \neq 5$ Therefore $t = y - 6; y \neq 5$